Chapter 12 - Vector-Valued Functions - Chapter 12 Review Exercises - Page 904: 34

$$\frac{1}{\|\mathrm{v}\|}(\mathrm{v} \cdot \mathrm{a})=\frac{d}{d t}(\|\mathrm{v}\|)$$

We find: \begin{array}{c} \mathrm{v}(t) \cdot \mathrm{v}(t) =\|\mathrm{v}\|^{2}\\ 2 \mathrm{v} \cdot \mathrm{a} =2\|\mathrm{v}\| \frac{d}{d t}\|\mathrm{v}\|\\ \frac{1}{\|\mathrm{v}\|}(\mathrm{v} \cdot \mathrm{a})=\frac{d}{d t}(\|\mathrm{v}\|) \end{array}